You should recall from Chapter 7 (Figure) that there is a yield surface in stress space that separates stress states that produce elastic responses from stress states that produce plastic responses. We are going to use the yield surface in (p9, q) space (Figure ) rather than (s91, s93) space so that our interpretation of soil responses is independent of the axis system.
Expansion of the yield surface
The yield surface is assumed to be an ellipse, and its initial size or major axis is determined by the preconsolidation stress, p9c. Experimental evidence (Wong and Mitchell, 1975) indicates that an elliptical yield surface is a reasonable approximation for soils. The higher the preconsolidation stress, the larger the initial ellipse. We will consider the yield surface for compression, but the ideas are the same for extension except that the minor axis of the elliptical yield surface in extension is smaller than in compression.
All combinations of q and p9 that are within the yield surface, for example, point A in Figure 11.3, will cause the soil to respond elastically. If a combination of q and p9 lies on the initial yield surface (point B,), the soil yields in a similar fashion to the yielding of a steel bar. Any tendency of a stress combination to move outside the current yield surface is accompanied by an expansion of the current yield surface, such that during plastic loading the stress point (p9, q) lies on the expanded yield surface and not outside, as depicted by C. Effective stress paths such as BC (Figure 11.3) cause the soil to behave elastoplastically.
If the soil is unloaded from any stress state below failure, the soil will respond like an elastic material. As the initial yield surface expands, the elastic region gets larger. Expansion of the initial yield surface simulates strain-hardening materials such as loose sands and normally and lightly overconsolidated clays. The initial yield surface can also contract, simulating strain-softening materials such as dense sands and heavily overconsolidated clays. You can think of the yield surface as a balloon. Blowing up the balloon (applying pressure; loading) is analogous to the expansion of the yield surface. Releasing the air (gas) from the balloon (reducing pressure; unloading) is analogous to the contraction of the yield surface. The critical state line intersects every yield surface at its crest. Thus, the intersection of the initial yield surface and the critical state line is at a mean effective stress prc/ 2 , and for the expanded yield surface it is at prG /2 .
Prediction of the Behavior of Normally Consolidated and Lightly Overconsolidated Soils Under Drained Condition:
Let us consider a hypothetical situation to illustrate the ideas presented so far. We are going to try to predict how a sample of soil of initial void ratio eo will respond when tested under drained condition in a triaxial apparatus, that is, a standard CD test. You should recall that the soil sample in a CD test is isotropically consolidated and then axial loads or displacements are applied, keeping the cell pressure constant. We are going to consolidate our soil sample up to a maximum mean effective stress p9c, and then unload it to a mean effective stress p9o such that Ro 5 prc /pro , 2. The limits imposed on Ro are only for presenting the basic ideas on CSM. More details on delineating lightly overconsolidated from heavily overconsolidated soils will be presented in Section.